I would be surprised if rear FSU wouldn't cause the same no sleep condition. There is no connection between no sleep and does it function. Wife's worked fine when it sucked the battery dead over night.

My understanding is it's a lot harder to get to than the front one so hopefully you can pull a fuse to test it

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)